The Buddhist concept of emptiness, or suññatā, has surprisingly important implications on the nature of discovery.
Emptiness, if you do not know, is a concept meaning that all phenomena lack inherent, independent existence. No thing can exist outside of other things. A stop sign for example depends on the color red which depends on our mind’s perception of red which depends on our brain which depends on conditioning & genetics which depends on our upbringing which depends on who raised us which depends on history… ok you get the picture.
Emptiness exists in EVERYTHING including big ideas about politics all the way down to the atoms of the screen you’re reading on. It is knowable in words, ideas, concepts, self-hood, knowledge, etc. It is considered to be the ultimate path to nirvana (liberation) by removing our avijjā (ignorance), relieving us of dukkha (suffering).
A word I like to use for emptiness is “illusory.” Meaning, when I call something empty, I am saying that thing is ultimately an illusion. The thing exists, but it also doesn’t. It’s like looking at an optical illusion. One side exists but is not the ultimate truth. And the ultimate truth doesn’t really exist either as it is dependent on your perspective. Someone looking at both sides of the illusion could call this the ultimate truth, but that perspective does not take into account for people seeing only one half of it. Find the middle way and transcend polarities.
For me, contemplating emptiness in everyday life has led me to dispel the illusion of boundaries and borders, specifically around concepts and ideas. This results in a very nice state of fluidity, like water. Ideas and concepts can move through me without getting stuck as a certain thing in existence that has to be a certain way. No longer am I burdened by the hard-stuck boundaries society likes to draw around things that keeps us from exploration.
Ultimately, I think this is what separates children from adults. Children have almost no conditioned boundaries in their mind. They play fantasy and imagination. They play with wonder and awe because no thing has yet to be boxed out of their perspective yet.
This is what Grothendieck meant when he said “discovery is the privilege of the child,” and “he is neither afraid that the things he looks at will have a bad taste, different from what he expects, from what they appear to be, or rather: from what he has already understood them to be.” The child he is describing is not bottlenecked by solid concepts or the way things should be. Things just appear in the children’s consciousness and play naturally emerges, because the possibilities are limitless. The child has no constraints on their perspective and respective actions, what occurs is just what occurs with little-to-no judgement.
The little child discovers the world as he breathes - the ebb and flow of his breath make him welcome the world in its delicate being, and makes him project himself into the world that also welcomes him. The adult can also discover, in those rare moments when he has forgotten his fears and his knowledge, when he looks at things or himself with eyes wide open, eager to know, new eyes - the eyes of a child.
This then is the power of emptiness— it helps us to take the perceptive of the child, of wonder and awe, while still holding onto useful concepts. But these concepts are held so lightly that if we want to, they are dropped as one would a feather. The weight is no longer burdening like that of a bowling ball. The phenomenological experience of working and thinking becomes fluid and light, but still grounded in reasoning and shared meaning.
If he is indeed confused, he has within him everything he needs to regain contact (as I once did) with the reality of things themselves, which he can know by first hand, rather than spinning like a squirrel trapped in an endless cage of words and concepts.
To realize the fruit of emptiness, it is important to have a meditation practice. Without one, someone can become deluded by their sense of fluidity without realizing what is actually occurring in their experience (one might be abstracting at a very high level without actually touching low levels of phenomenology which leads to delusion and bypassing). It’s hard to put into words the amount of power a regular meditation habit gives, but if I had to describe it, it’s like re-discovering the first principles of my experience and being able to manipulate what’s going on on a low level to serve me better. And all this is done by achieving deeper and deeper insights about emptiness, ultimately leading to insights about knowledge and discovery. Most of these insights occur as felt senses rather than things easily put into words.
To further illustrate the power of emptiness, here is another Grothendieck quote outlining why his peers were not as successful as him in terms of discovery:
In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone.
In other words, Grothendieck realized emptiness by his ability to be alone and re-discover himself from first principles. Literally just look at the last sentence— “To have broken these bounds.” His peers would have been more successful if they could have gone outside their own boundaries, their own constraints. Grothendieck had the ability to take the perspective of a child due to his capacity to be alone.
As one spends time in solitude, they no longer bump up against other boundaries in their experience like they would if they were surrounded by their peers. Solitude gives us almost a sandbox mode for life (a sandbox video game gives users lots of freedom, free of linear goals and hard rules) we otherwise could not operate in. Being with others and working with them is especially important, probably even more so than solitude, but they are two entirely different modes of being. Working alone gives us a whole new way of working, of thinking, of looking at the world. Even if we do work on amazing teams that foster creativity and open-mindedness, that experience is still no where close to what you can get when working by yourself free from others (this is also made more obvious with a meditation practice).
How many are there, including among the unfortunate "researchers" themselves, in need of theses or articles, including even among the most "scholarly", most prestigious among us - those who has the naivety to see that "research" is neither more nor less than questioning things, passionately - like a child who wants to know how he or his little sister came into the world. To search and to find, that is to say: to question and to listen is the simplest, most natural thing in the world, in which no one in the world has a privilege. It is a "gift" that we all have received since the cradle - made to express and flourish with an infinity of faces, from one moment to another and from one person to another...
Notice here how Grothendieck says “to question and to listen is the simplest, most natural thing in the world.” This is what the child does when not stuck in a solid state of conditioning like adults are. This is why adults have a harder time doing this (to question and listen), for we do not realize the wisdom of emptiness, of the illusory nature of what we think reality is, which naturally leads us to a fate we have decided for ourselves. And we decide to bask in this fate as if it is deterministic, as if we do not have the agency to return to that state of awe and naturality.
My relationship to mathematics (and especially to mathematical achievement) was heavily weighted by ego, and this was not the case with Mike. He really gave the impression of doing maths like a kid having fun, while also not forgetting to eat and drink.
This is the ultimate goal of contemplating and realizing emptiness when it comes to knowledge and discovery. Hold boundaries very lightly (do maths like a kid having fun), but keep yourself grounded in good sensemaking (don’t forget to eat and drink) by being able to freely climb levels of abstraction. This process allows us to use concepts and ideas to our advantage, but transcend any solidity we might dawn on ourselves.
I think this is laid out best by Roger Thisdell:
Sanity = Lucidly climbing up & down the branches of abstraction
A big source of confusion I spot in people is when they get stuck attending to reality at stifling levels of abstraction; either by going too complex or too simple, and not being able to scale to a different level when that would get them out of a confuddlement.
"Everything is Yin and Yang! No, it's all One! No, it's neither, it's non-dual! But my five family members are coming over for dinner and I need to remember to buy 14 items at the supermarket, and calculate my taxes. And my brother is probably going to bring up politics which is so overwhelming complicated! But it's all One..."
So many minds get stuck trying to figure out the forest, when maybe what they really need to do is look at the individual trees. Or sometimes they need to get down to ground level and pick through the dirt, or sometimes take a bird's eye view of the canopy, except they're stuck or don't realise everything else has moved on.
The mind chunks and fuses reality all the time - you may have noticed. But how much have you really noticed, and how much flexible control do you have over this process? At least become lucid of it.
I have found that by recognizing this feature of mind, and becoming better at navigating strata of abstraction, my sense of clarity and sanity has gone way up.
Great spiritual development is to be able to nimbly both reach lower on the levels of abstractions - all the way to zero* - AND be able to hold onto higher and higher levels of abstraction, extending our consciousness capacity, before we project to infinity (aka 'more than I can make sense of').
The next time you are contemplating a problem or trying to find new discoveries, it might be helpful to asses how emptiness can help you. What is your perspective dependent on? Conditioning? Mood? Framing? Are you drawing any hard boundaries where they could be dropped? What about just looking at the problem for 5 minutes from a totally different lens? Is your ego playing a role? What about societal expectations? What if you generated genuine questions about problem rather than questions from a place of having to find an answer? What if there was no answer?